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The Resistance Training
Dose-Response:
Meta-Regressions Exploring the
Preprint
not peer reviewed
Supplementary materials:
https://osf.io/6z3xu
For correspondence:
jpelland2020@fau.edu
Effects of Weekly Volume and
Frequency on Muscle
Hypertrophy and Strength Gain
Joshua C. Pelland1, Jacob F. Remmert1, Zac P. Robinson1, Seth Hinson1, Michael C. Zourdos1
1
Department of Exercise Science and Health Promotion, Florida Atlantic University
Please cite as: Pelland, J., Remmert, J., Robinson, Z., Hinson, S., Zourdos, M. (2024). The Resistance
Training Dose-Response: Meta-Regressions Exploring the Effects of Weekly Volume and Frequency
on Muscle Hypertrophy and Strength Gain. SportRχiv.
All authors have read and approved this version of the
manuscript. This article was last modified in September 2024.
ABSTRACT
Background: Weekly set volume and frequency are used to manipulate resistance training
(RT) dosage. Previous research has identified higher weekly set volume as enhancing
muscle hypertrophy and strength gains, but the nature of the dose-response relationship
still needs to be investigated. Mixed evidence exists regarding the effects of higher weekly
frequency.
Objective: Before meta-analyzing the volume and frequency research, all contributing RT
sets were classified as direct or indirect, depending on their specificity to the
hypertrophy/strength measurement. Then, weekly set volume/frequency for indirect sets
was quantified as 1 for ‘total,’ 0.5 for ‘fractional,’ and 0 for ‘direct.’ A series of multi-level
meta-regressions were performed for muscle hypertrophy and strength, utilizing 67 total
studies of 2,058 participants. All models were adjusted for the duration of the intervention
and training status.
Results: The relative evidence for the ‘fractional’ quantification method was strongest;
therefore, this quantification method was used for the primary meta-regression models.
The posterior probability of the marginal slope exceeding zero for the effect of volume on
both hypertrophy and strength was 100%, indicating that gains in muscle size and strength
increase as volume increases. However, both best fit models suggest diminishing returns,
with the diminishing returns for strength being considerably more pronounced. The
posterior probability of the marginal slope exceeding zero for frequency’s effect on
hypertrophy was less than 100%, indicating compatibility with negligible effects. In contrast,
the posterior probability for strength was 100%, suggesting strength gains increase with
increasing frequency, albeit with diminishing returns.
Conclusions: Distinguishing between direct and indirect sets appears essential for
predicting adaptations to a given RT protocol, such as using the ‘fractional’ quantification
method. This method’s dose-response models revealed that volume and frequency have
unique dose-response relationships with each hypertrophy and strength gain. The
dose-response relationship between volume and hypertrophy appears to differ from that
with strength, with the latter exhibiting more pronounced diminishing returns. The
dose-response relationship between frequency and hypertrophy appears to differ from
that with strength, as only the latter exhibits consistently identifiable effects.
1 INTRODUCTION
Resistance training (RT) outcomes depend on many factors, including the configuration of
programming variables. Two variables, volume and frequency, are important for
manipulating the RT dosage. Understanding the dose-response relationships between
these variables and muscle hypertrophy and muscle strength gains is essential for making
well-informed programming decisions.
Weekly RT set volume has been deemed a primary program design variable and therefore
received considerable attention (1–4). Indeed, multiple meta-analyses have reported that
the number of RT sets per muscle group per week has a positive dose-response
relationship with muscle hypertrophy (1,5,6) and strength gains (7). However, many of
these analyses explore a specific range of volumes and have limited conclusions due to a
paucity of data at the time of analysis. For example, in 2017, Ralston et al. (7)
meta-analyzed the effects of set volume, reporting greater strength gains with > 5 weekly
sets compared to ≤ 5 weekly sets (SMD: 0.18 [95% CI: 0.06, 0.30]; p = 0.003). Therefore, this
analysis does not address the higher end of the dose-response relationship. Similarly in
2017, for muscle hypertrophy, Schoenfeld et al. (1) reported greater improvements, albeit
non-significantly (p = 0.076), in RT groups performing ≥ 9 sets per muscle group per week
(ES: 0.46 [95% CI: 0.21, 0.71]) compared to groups performing < 9 sets per muscle group
per week (ES: 0.32 [95% CI: 0.19, 0.46]). However, the authors noted conclusions could not
be made regarding the dose-response relationship for greater than 9 weekly sets due to a
paucity of data.
In 2020, with more data available, Baz-Valle et al. (5) explored the effects of 12-20 vs. 20+
weekly sets on hypertrophy, reporting that 20+ sets resulted in significantly more
hypertrophy in the triceps brachii (SMD: -0.50 [95% CI: -0.88, -0.11]; p = 0.01) but not in the
biceps brachii (SMD: -0.10 [95% CI: -0.46, 0.26]; p = 0.59) or quadriceps femoris (SMD: -0.20
[95% CI: -0.49, 0.10]; p = 0.19). Currently, readers looking to gain specific insight into the
dose-response relationship between weekly RT set volume and hypertrophy may
triangulate the results from Schoenfeld et al. (1) and Baz-Valle et al. (5), perhaps concluding
that there are substantial diminishing returns beyond ~12-20 sets per muscle group per
week. However, there are limitations to this interpretation, particularly given the
categorical nature of these analyses. For example, comparing 10-20 weekly sets to 21-30
weekly sets wouldn’t capture meaningful differences within the same arbitrary range (e.g.,
21 vs. 30 weekly sets). Further, it has been suggested that the dose-response relationship
may follow an inverted-U-shaped curve, in which additional volume eventually results in a
plateau and ultimately a detrimental impact on muscular adaptations (4). To rectify these
limitations, we propose that volume be treated as a continuous variable (8,9) to gain insight
into the magnitude and functional form of the dose-response relationship.
Furthermore, previous meta-analyses have quantified all sets for a given muscle group as
equal whether it is the primary force generating muscle (e.g., pectoralis major in the bench
press) or a synergist muscle (e.g., triceps brachii in the bench press). However, some data
suggest synergists may experience less hypertrophy than the primary force generator
(10,11). Nonetheless, the evidence remains unclear regarding how to quantify synergist
muscle set volume accurately (12,13). Regarding muscle strength, no meta-analysis has
explored the contribution of non-specific exercises training the muscles involved in the
strength assessment (e.g., leg press training for squat one repetition maximum [1RM]).
Therefore, the dose-response relationship with different quantification methods, such as
counting sets for synergist muscles/non-specific exercises as half of a set, still needs to be
explored (12).
Similar limitations in the volume research apply to research examining the effects of
frequency (i.e., the number of times per week a muscle or exercise is trained) on muscle
hypertrophy and strength gains. Meta-analyses on the effects of frequency have produced
mixed results but generally suggest no independent effect of higher frequencies (14–19).
Moreover, meta-regressions of volume-equated studies have yielded non-significant results
for hypertrophy (14) and strength (17); however, to our knowledge, only linear
meta-regressions have been performed. Thus, other functional forms should be considered
to elucidate potential nonlinear effects.
Therefore, the purpose of this meta-analysis was to explore the nature of the continuous
dose-response relationships between weekly set volume and muscle hypertrophy, weekly
set volume and muscle strength gains, weekly frequency and muscle hypertrophy, and
weekly frequency and muscle strength gains using various quantification methods.
2 METHODS
This meta-analysis was conducted according to Preferred Reporting Items for Systematic
Reviews and Meta-Analyses guidelines (20). Pre-registration on the Open Science
Framework (https://osf.io/r958n) using the International Prospective Register of Systematic
Reviews template was used, though some of the methods have changed since the original
pre-registration.
2.1 Inclusion Criteria
Inclusion criteria included studies, pre-prints, theses, or abstracts (author correspondence
permitting) 1) published or pre-printed before June 2024; 2) available in English; 3)
employed a dynamic RT intervention with eccentric and concentric training utilizing a
randomized experimental design (either within- or between-group) lasting a minimum of 4
weeks in healthy participants; 4) did not involve participants > 70 years old; 5) compared at
least two groups featuring differences in set volume and/or frequency while controlling for
the load (±5% of 1RM or ±2RM) and proximity to failure (failure, non-failure, or mixed); 6)
included pre-intervention and post-intervention measurements of muscle hypertrophy
with a direct, site-specific measurement (ultrasound, computed tomography, magnetic
resonance imaging, muscle biopsies) or included pre-intervention and post-intervention
measurements of dynamic (up to a 10RM), isometric, or isokinetic maximal strength; 7) not
retracted or called into question by Vigotsky et al. (21).
2.2 Search Strategy
PubMed/Medline and Google Scholar databases were searched for studies until April 2023.
The following search terms were used for PubMed/Medline: ("resistance training" OR
"resistance exercise" OR "strength training") AND ("musc*" OR "hypertrophy" OR "muscle
mass" OR "muscle thickness" OR "growth" OR "cross sectional area" OR "fat free mass" OR
"lean body mass" OR "limb circumference" OR "muscle strength" OR "strength") AND
("volume" OR "dose" OR "dose response" OR "frequency" OR "multiple sets" OR "single
sets" OR "sessions per week" OR "sessions"). The following search terms were used for
Google Scholar: allintitle: ("resistance training" OR "resistance exercise" OR "strength
training") AND ( "musc *" OR hypertrophy OR "muscle mass" OR "muscle thickness" OR
growth OR "cross sectional area" OR "fat free mass" OR "lean body mass" OR "limb
circumference"). Screening was performed using abstrackr
(http://abstrackr.cebm.brown.edu). Titles, abstracts, and full texts were examined for
inclusion; data was extracted from full texts that met the inclusion criteria. JP and JR
performed this process. Following screening and exclusion of studies deemed not to meet
the inclusion criteria, the reference lists of included studies and publications that cited the
included studies were also screened for inclusion. Finally, studies published between April
2023 and June 2024 authors became aware of were included.
2.3 Quality Assessment
The quality of the included studies was assessed using the TESTEX scale (22), designed
specifically for exercise training studies. In addition to the pre-registered primary
meta-regressions modeling the effect of a given set volume/frequency, three analyses were
added to aid in interpretation of the effects: 1) funnel plots and effective sample size
approximated bias-adjusted estimates (23) for assessing heterogeneity and small study
bias (24), 2) contrast-based meta-analyses to assess the consistency of effects between
higher vs. lower volume/frequency, 3) additional meta-regressions with strict inclusion
criteria, described in section 3.
2.3 Data Extraction
Data was extracted/coded and included variables regarding study design, measurements,
participant descriptives, RT protocol descriptives, and outcomes. Where data were not
available in the full text, attempts were made to contact authors to request missing data. If
there was no response, data was obtained using WebPlotDigitizer (v5.0, Ankit Rohatgi)
where possible. RT protocol descriptive data were extracted as separate variables for ‘total,’
‘fractional,’ and ‘direct’ volume and frequency classifications.
2.4 Volume and Frequency Classifications (‘Total’/’Fractional’/’Direct’)
All RT sets were classified as direct or indirect, allowing for three classifications of RT
variables (‘total’/‘fractional’/‘direct’). ‘Total’ was the sum of direct and indirect sets,
‘Fractional’ counted indirect sets as half a set (indirect × 0.5 + direct), and ‘direct’ did not
account for indirect sets.
For hypertrophy, direct sets were those in which the measured muscle(s) was likely to be
the primary force generator in the exercise. Indirect sets were those in which the measured
muscle(s) was likely to be meaningfully trained but not the primary force generator of the
exercise (i.e., synergist). For example, a study measuring biceps brachii hypertrophy
consisting of 5 sets of biceps curls in one session and 5 sets of rows in another session
would result in a weekly volume quantified as ‘total,’ ’fractional,’ and ‘direct’ of 10, 7.5, and
5, respectively. This example would result in frequency quantified as ‘total,’ ‘fractional,’ and
‘direct’ of 2, 1.5, and 1, respectively.
For strength, direct sets were those that trained the exact exercise used for the strength
assessment. Indirect sets were any that were likely to meaningfully train the muscle(s)
involved in the strength assessment. This includes the primary force generator and
synergists for the strength assessment. For example, a study measuring back squat 1RM
strength consisting of 5 sets of back squats in one session, 5 sets of back squats in a
second session, and 5 sets of leg presses in a third session would result in a weekly volume
quantified as ‘total,’ ‘fractional,’ and ‘direct’ of 15, 12.5, and 10, respectively. This example
would result in frequency quantified as ‘total,’ ‘fractional,’ and ‘direct’ of 3, 2.5, and 2,
respectively.
This process was not wholly objective; therefore, table 1 reports the decisions made
throughout the included studies to clarify the methods used and aid in interpretation. In
addition to volume and frequency, RT protocol descriptives (i.e., repetition range, interset
rest, etc.) were weighted in accordance with ‘total,’ ’fractional,’ and ’direct’ classifications
using a custom calculator.
2.5 Control Group Estimates and Smallest Detectable Effect Size
Rather than omitting non-training control groups from our analysis, potentially discarding
valuable information, their effects were included to improve power/precision and more
realistically anchor the magnitude of model estimates. However, non-training control group
data was only included from studies using untrained participants as the effects from
studies using previously trained participants represent de-training protocols.
Further, to contextualize the results within sources of error present in RT studies, our
intention was to utilize the extracted data from untrained, non-training control groups in
the included studies to inform a smallest detectable effect size (SDES). However, only 13
included studies (25–37) featured untrained, non-training control groups, and this was
particularly problematic given only two of these studies included hypertrophy measures
(25,26). Therefore, we utilized untrained, non-training control group effect estimates from
124 strength studies (368 effects) and 69 hypertrophy studies (223 effects) from data made
available by Steele et al. (38) to approximate errors associated with longitudinal RT studies.
Specifically, the square root of the sum of the estimated variance components from a
multi-level mata-analytic model was used as the SDES. This value is 2.05% and 3.96% for
hypertrophy and strength, respectively (https://osf.io/3e67h).
Table 1A: Exercises Counted as Direct and Indirect Weekly Set Volume for Hypertrophy
Muscle(s) Assessed
Measurement(s) Direct Exercise(s)
Quadriceps, Knee Extensors, Lateral
Thigh, Anterior/Middle Thigh, Vastus
Lateralis, Vastus Medialis, or Vastus
Intermedius
MT, Sum of MT, CSA,
Fiber Area, Muscle
Volume
Indirect Exercise(s)
Back Squat, Leg Press, Dumbbell Lunge, Leg
Extension, Hack Squat, Smith Machine Squat,
Barbell Split Squat, Dumbbell Split Squat, Bulgarian
N/A
Split Squat
MT, CSA,
Rectus Femoris
Ultrasound-Derived
Leg Extension
Smith Machine Squat, Leg Press, Squat
Leg Curl
N/A
N/A
Circumference
Hamstrings or Posterior Thigh
MT, CSA, Muscle
Volume
Pectoralis Major
MT
Bench Press, Flat Dumbbell Fly
Anterior Deltoid
MT
Barbell Shoulder Press, Barbell Shoulder Front Raise Bench Press, Chest Press, Barbell Close Grip Press On Bench
Trapezius
CSA
N/A
Tricep Push-Down, Triceps Extension, Tricep
Triceps Brachii or Elbow Extensors
MT, Muscle Volume
Kickback, Skullcrusher, Lying Triceps Press, Lying
Tricep Extension, Cable Overhead Extension,
Overhead Dumbbell Extensions, Close Grip Bench
Biceps Brachii or Elbow Flexors
MT, CSA, Muscle
Volume
Bicep Curl, Dumbbell Bicep Curl, Hammer Curl,
Dumbbell Incline Curl, Barbell Preacher Curl,
Dumbbell Preacher Curl, Machine Curl
Lat Pulldown, Seated Row
Flat Bench Press, Incline Bench Press, Decline Bench Press,
Shoulder Press, Dumbbell Shoulder Press, Incline Dumbbell Press,
Incline Machine Press, Machine Press
Lat Pulldown, Neutral Grip Lat Pulldown, Supine Grip Pulldown,
Machine Lat Pulldown, Seated Row, Close-Grip Machine Row,
Wide-Grip Machine Row, Bent-Over Barbell Row, Supine Grip
Bent-Over Row
Effort was made to use similar verbiage as manuscripts to best represent the classification decisions. MT = muscle thickness; CSA = cross-sectional area.
Table 1B: Exercises Counted as Indirect Weekly Set Volume for Strength
Strength
Measurement(s)
Indirect Exercise(s)
Back Squat
1RM, 10RM
Leg Extension, Barbell Split Squat, Dumbbell Split Squat, Bulgarian Split Squat, Hack Squat, Dumbbell Lunge, Leg Press
Smith Machine Squat
1RM
Leg Press, Leg Extension
Assessment
Leg Press
1RM, 5RM, 10RM,
Estimated 1RM
Dumbbell Lunge, Leg Extension
Hack Squat
1RM
Back Squat
Leg Extension
1RM, Estimated 1RM
Squat, Leg Press
Leg Extension Isometric
Peak Torque
Leg Extension (Dynamic), Leg Press, Squat
Leg Extension Isokinetic
Peak Torque
Leg Extension (Dynamic), Squat, Leg Press, Barbell Lunge
Deadlift
1RM
Romanian Deadlift
Romanian Deadlift
Estimated 1RM
N/A
Leg Curl
1RM, 10RM
N/A
Leg Flexion Isometric
Peak Torque
Leg Curls (Dynamic)
Leg Flexion Isokinetic
Peak Torque
Leg Curls (Dynamic), Romanian Deadlift
Calf Raise
1RM
N/A
Torso Rotation Isometric
Peak Torque
Torso Rotation (Dynamic)
Back Extension Isometric
Peak Torque
Back Extension (Dynamic)
Close Grip Bench Press, Bench Press Machine, Chest Machine Press, Incline Bench Press, Incline Dumbbell Press, Incline Bench
Press Machine, Incline Machine Press, Decline Bench Press, Shoulder/Overhead Press, Behind Neck Seated Shoulder Press,
Bench Press
1RM, 5RM, Estimated
Machine Shoulder Press, Tricep Push-Down, Machine Triceps Extension, Tricep Kickback, Skullcrusher, Lying Triceps Press, Barbell
1RM
Lying Arm Extension, Cable Overhead Extension, Triceps Extension, Dumbbell Tricep Extension, Tricep Pushdown, Dumbbell
Overhead Extension, One Arm Triceps Extension, Flat Dumbbell Fly, Cross Cable Fly, Pec-Dec Fly, Pec Fly, Barbell Shoulder Front
Raise, Front Dumbbell Raise
Smith Machine Bench
Press or Chest Press
1RM, 10RM
Shoulder Press, Bench Press, Arm Cross (Pec-Dec) Machine, Overhead Press Machine, Tricep Extension Machine
Bench Press Isometric
Peak Force
Bench Press (Dynamic), Shoulder Press
Shoulder Press
1RM, 5RM, 10RM
Chest Press, Bench Press, Tricep Extension, Incline Bench Press, Behind Neck Seated Shoulder Press, Lateral Raise, Upright Row
Estimated 1RM
Bench Press
Overhead Press Machine
1RM
Chest Press, Lateral Raise Machine, Tricep Extension Machine
Upright Row
1RM
Lateral Raise, Posterior Lateral Raise
Lateral Raise
1RM
N/A
Bent Over Row
1RM
Bicep Curl, Lat Pulldowns
1RM, 10RM, Estimated
Wide-Grip Seated Row, Lat Pulldown, Neutral Grip Lat Pulldown, Dumbbell Hammer Curl, Machine Lat Pulldown, Dumbbell Incline
1RM
Curl, Dumbbell Preacher Curl, Bicep Curl
Machine
Dumbbell Overhead
Press
Seated Row
Lat Pulldown
1RM, 5RM, 10RM,
Estimated 1RM
Seated Row, Bicep Curls, Rowing, Supinated Bent-Over Row
Tricep Press
1RM
Bench Press
Lying Triceps Extension
1RM
N/A
Peak Torque
Barbell Bench Press, Seated Chest Press, Lying Barbell Triceps Extensions, Triceps Extension
Elbow Extension
Isokinetic
Lat Pulldown, Seated Row, Supinated Lat Pulldown, Lat Rowing, Machine Bicep Curl, Supinated Bent-Over Row, Dumbbell Bicep
Bicep Curl
1RM
Bicep Curl Machine
1RM
N/A
Elbow Flexion Isometric
Peak Torque
Bicep Curls (Dynamic), Supinated Bent-Over Row, Supinated Lat Pulldown
Elbow Flexion Isokinetic
Peak Torque
Lat Pulldown, Seated Row, Bicep Curl, Standing Barbell Bicep Curl, Scott Bench Bicep Curl
Curl, Dumbbell Hammer Curl
Effort was made to use similar verbiage as manuscripts to best represent the classification decisions. RM = repetition maximum.
3 STATISTICAL ANALYSIS
This meta-analysis was performed using the brms and metafor packages in the R language
and environment for statistical computing (v 4.0.2; R Core Team, https://www.r-project.org).
The extracted dataset, analysis scripts, estimates, plots, and supplementary materials are
available on the Open Science Framework (https://osf.io/6z3xu). Given the goal of this
analysis, we have opted to avoid dichotomizing our findings and therefore did not employ
traditional null hypothesis significance testing (39). Rather, we took an estimation-based
approach within a Bayesian framework in which effect estimates and their precision were
interpreted continuously and probabilistically (40). As many of the included studies had
multiple groups and reported effects within these groups for multiple outcomes, we opted
to calculate effect sizes in a nested structure.
Therefore, for our primary analyses, multilevel arm-based meta-regression models (41,42)
were performed with study, group, and observation included as nested random intercepts
in the model (i.e., observations were nested within groups which were nested within
studies). To account for potential heterogeneity in the fixed effects between studies, we
planned to include random slopes on the study-level for the dose-related variables (i.e.,
volume/frequency). However, in nearly all cases there were unresolvable model warnings
(e.g., divergent transitions); thus, random slopes were omitted in favor of model
parsimony. Effects were weighted by inverse sampling variance to account for the
observation-level, within-study, and between-study variance. Models were constructed with
effect sizes, and variances thereof, calculated as response ratio using the escalc function
(43,44). Specifically, response ratios were calculated as the sum of the natural logarithm of
the ratio of post-test and pre-test means, which were later exponentiated (i.e., ex) and
thereby converted to percentage change scores to aid practical interpretation. Importantly,
because typical standardized mean differences (i.e., hedges’ g) and response ratios operate
on different scales (i.e., additive vs. multiplicative) that may have implications on model
selection (45), we also calculated effect sizes as a standardized mean change or the
difference between post-test and pre-test means, divided by the pooled pre-test standard
deviation with an adjustment (i.e., C) for small sample bias. Formulas for each effect size
and their variances can be seen below:
(
𝑆𝑀𝐶 = 𝐶
𝑀𝑒𝑎𝑛𝑝𝑜𝑠𝑡 − 𝑀𝑒𝑎𝑛𝑝𝑟𝑒
𝑣𝑎𝑟(𝑆𝑀𝐶) =
𝑆𝐷𝑝𝑟𝑒
2(1 − 𝑟)
𝑛
+
)
; 𝐶=1 −
(𝑆𝑀𝐶)
2 ·𝑛
2
(
3
4(𝑛−1) − 1
)
(
𝑅𝑅 = 𝑙𝑛
𝑀𝑒𝑎𝑛𝑝𝑜𝑠𝑡
𝑀𝑒𝑎𝑛𝑝𝑟𝑒
𝑣𝑎𝑟(𝑅𝑅) =
)
(𝑆𝐷𝑝𝑜𝑠𝑡)
2
𝑛 · (𝑀𝑒𝑎𝑛𝑝𝑜𝑠𝑡)
2
+
(𝑆𝐷𝑝𝑟𝑒)
2
𝑛 · (𝑀𝑒𝑎𝑛𝑝𝑟𝑒)
2
−
2 · 𝑟 · (𝑆𝐷𝑝𝑜𝑠𝑡)· (𝑆𝐷𝑝𝑟𝑒)
𝑛 · (𝑀𝑒𝑎𝑛𝑝𝑜𝑠𝑡) · (𝑀𝑒𝑎𝑛𝑝𝑟𝑒)
( 𝑙𝑛𝑅𝑅 − 1) * 100
𝑅𝑅𝑒𝑥𝑝 = 𝑒
Few studies reported the pre-intervention to post-intervention correlations required to
determine the variance for the effect sizes. Therefore, the available data were used to
retroactively calculate pre-to-post correlations if possible (46). Then, we took the median of
these approximated correlation coefficients and imputed this estimate for the studies
where we were unable to obtain the required data. Similarly, if the standard deviations
needed to calculate the effect sizes were missing, approximation methods were used via
referencing a weighted coefficient of variation (47). Marginal and conditional R2 were
calculated to quantify the proportion of variance explained by only the fixed effects and the
sum of the fixed and random effects, respectively (48).
To account for potential nonlinear dose–response relationships between volume/frequency
and RT outcomes, the following functional forms for all model structures described above
were preliminarily fit with the metafor package as random intercept models with both type
of effect sizes and subsequently compared using the performance package (49), utilizing a
Bayesian Information Criterion (BIC) approximated Bayes Factor to determine under which
model the observed data are the most probable for each outcome (i.e., muscle
hypertrophy and strength). Importantly, a Bayes Factor was calculated for each model
relative to an intercept-only model and subsequently averaged between effect sizes. The
model that performed the best after accounting for effect sizes on both additive and
multiplicative scales was considered the “best fit”:
1. Linear
2. Restricted Cubic Spline (4 knots)
3. Linear-log
4. 2nd Order Polynomial
5. Square Root
6. Quadratic Term
7. Reciprocal
While both effect sizes were used for model selection, response ratio models are reported.
All models included the following fixed effects: 1) weekly set volume or frequency (‘total,’
’fractional,’ or ’direct’), 2) a linear term of frequency in volume models or volume in
frequency models, 3) duration (i.e., weeks) of the training intervention (continuous), and 4)
training status of the participants (binary categorical).
Marginal effects (means) with 95% compatibility intervals (quartile-based credible and
prediction intervals) were extracted for the main effect of weekly set volume or frequency
(adjusted proportionally for all other predictors) using the emmeans package (50). To better
approximate the absolute magnitude of all model predicted effect sizes, all presented
estimates have been control adjusted in that the mean effect size predicted at a dose of 0
was contrasted with the mean effect size predicted at every other dose. Therefore, the
models represent effect sizes and compatibility intervals of a given volume/frequency value
relative to the control effect.
Following the determination of the best fit volume models for each outcome (i.e., muscle
hypertrophy or strength), interaction moderator analyses were performed with the metafor
package to investigate the influence of a variety of factors related to study design and
participant characteristics primarily for future hypothesis generation. Specifically, separate
models were fit for each moderator that maintained the same structure as the best fit
model from the primary analysis, but also included a linear main effect and interaction
term between weekly set volume and the moderator of interest (i.e., age, sex, proximity to
failure, etc.). Given differences in the number of effects between levels of the moderator,
non-training control groups and effects from frequency studies were not included to
ensure undue weight was not provided to these effects.
To answer the research questions, our data set included studies that manipulated training
volume and/or frequency. Therefore, the primary volume meta-regression models also
included data from studies manipulating frequency. Similarly, the primary frequency
meta-regression models also included data from studies manipulating volume. The
inclusion of these indirect effects improves statistical power/precision and thus the ability
to detect small but potentially practically relevant effects (51). Although between-study
heterogeneity such as these design characteristics are explicitly accounted for in the
multilevel structure and fixed effects of the primary meta-regression models, efforts were
made to also acknowledge strict inclusion criteria approaches (i.e., only direct
comparisons). Specifically, traditional multilevel contrast-based meta-analytic models were
fit utilizing between condition effect sizes. First, we examined an intercept only model
which compared “higher” vs. “lower” volumes/frequencies. Additionally, two-stage
fixed-effect meta-regression models were performed. In the first stage, independent
sample size weighted linear models were fit for each outcome within each study, extracting
the intercept and slope for each and then pooled per study. These estimates were then
again weighted by sample size and pooled for each study in a multivariate model allowing
for the residual correlations between the intercepts and slopes to be accounted for. In the
second stage, the intercepts and slopes were meta-analyzed across studies again using a
multivariate model to account for the residual correlation between estimates. The
posterior distributions of the pooled intercept and slope were utilized to create
dose-response predictions. A linear form was used for both stages due to limitations of the
number of observations included per regression model in stage one. We view the purpose
of these additional meta-analytic approaches that only utilize direct comparisons as
verification that the primary meta-regression models are not unduly biased in some way by
confirming their directionality and magnitude do not differ substantially from the models
that only contain direct comparisons. This verification is with the understanding that these
models contain far fewer observations and thus will have less precision in their effect
estimates, on average, and potentially lose the beneficial aspects of effect regularization
from partial pooling and shrinkage featured in the primary models. There was not an
irreconcilable contradiction in the results of any of the best fit models; however, these
models potentially aid in interpretation.
Finally, to assess the relative evidence for each volume/frequency quantification method
(‘total’/’fractional’/’direct’), Bayes Factors for each pairwise comparison between primary
meta-regression models were calculated. The resulting Bayes Factor provided a measure of
the relative evidence of which model (i.e., method of quantifying volume/frequency) was
the most probable given the available data. The strength of evidence was interpreted
based on the Kass and Raferty scale (52).
4 RESULTS
4.1 Search Results
Figure 1 details the search process (53). The search strings identified 6,677 publications for
potential inclusion. Citation searching yielded 16 additional studies for screening, and this
included studies the authors became aware of upon publication after April 2023. Once
duplicates were removed, 6,515 studies remained. After title and abstract screening, 135
publications remained. Finally, full texts were assessed for eligibility, and 67 studies were
included. In cases where the manuscript provided insufficient information for data
extraction, attempts were made to contact the authors to gain further information and
include the publication.
4.2 Quality Assessment
The mode TESTEX score was 12/15 (range = 8-14/15; https://osf.io/z6rtb). The mode study
quality score was 3/5 (range = 1-5/5). The mode study reporting score was 8/10 (range =
4-10/10). Qualitative assessment of funnel plots and effective sample size approximated
bias-adjusted estimates did not indicate small-study bias. Contrast-based meta-analyses
and two-stage meta-regressions returned no consistent indication of larger-than-expected
heterogeneity in results. These analyses can be found in the supplementary materials
(https://osf.io/6z3xu).
4.3 Study Characteristics
A breakdown of the 67 studies (25–37,54–107) consisting of 2,058 participants included in
this analysis can be found in the supplementary files (https://osf.io/86g9r). Training
interventions lasted 10.42 ± 4.48 weeks and the age of the participants was 25.16 ± 5.22
years. Twenty eight studies included untrained participants and 39 studies included trained
participants. A visual summary of the training interventions from the included studies can
be seen in Figure 2. The median values of the primary RT variables in training groups (i.e.,
excluding control effects) for muscle hypertrophy effects, using the ‘fractional’
quantification method, were as follows: volume–10.5 sets per week; frequency–2 sessions
per week; interset rest–1.75 minutes; average repetitions per set–10. The average values
for these metrics were 13.00 ± 8.87 sets per week, 2.33 ± 0.98 sessions per week, 1.80 ±
0.68 minutes, and 10.63 ± 3.53 repetitions per set. Regarding training groups for muscle
strength effects, the median values were 6 sets per week, 2 sessions per week, 2 minutes,
and 10 repetitions per set. The average values for these metrics were 8.14 ± 6.23 sets per
week, 1.97 ± 0.92 sessions per week, 2.04 ± 0.79 minutes, and 9.85 ± 3.19 repetitions per
set. The majority of effects utilized protocols with some sort of failure definition (e.g.,
momentary/concentric/muscular/volitional failure, 0 repetitions in reserve, repetition
maximum) definition; 78.47% of effects were categorized as failure training for hypertrophy
and 78.12% for strength. When reported, the time between the final RT session and
post-testing muscle size assessments was ≥ 48 hours for 96.07% of hypertrophy effects;
however, 30.45% of effects did not report this information. A visualization of muscle size
assessment timelines can be found in the supplementary materials (https://osf.io/gx2zn).
Figure 1: PRISMA Flow Diagram
0
10
20
30
40
50
0
Weekly Sets
0
10
20
30
Weekly Sets
1
2
3
4
5
6
0
Weekly Frequency
40
50
0
1
2
3
4
5
Weekly Frequency
10
20
30
0
Average Repetitions Per Set
6
0
10
20
Average Repetitions Per Set
1
2
3
4
5
Average Interset Rest (min)
30
0
1
2
3
4
Average Interset Rest (min)
failure
mixed
nonfailure
Proximity to Failure
5
failure
mixed
nonfailure
Proximity to Failure
Figure 2: Raincloud plots providing a visual summary of 220 hypertrophy (blue) and 490 strength (orange) effects included in the analysis. Each data point
represents an effect. Values were weighted in accordance with the ‘fractional’ volume quantification method. Regarding repetitions per set, non-training control
effects are not displayed and one data point at 51 repetitions for both hypertrophy and strength is not displayed for visual ease. Regarding interset rest, nontraining control effects and single-set protocols are not displayed; additionally, 4 hypertrophy and 62 strength effects did not have a value (insufficient reporting).
Regarding proximity to failure, non-training control effects are not displayed; additionally, 16 strength effects did not have a value (insufficient reporting).
4.4 Volume/Frequency Quantification Method Comparison
Meta-regressions for each volume/frequency quantification method
(‘total’/’fractional’/’direct’) were modeled for each strength and hypertrophy. The analysis of
the relative evidence for each best fit model in terms of 2 x Log(Bayes Factor[BF]) values
(52) is presented in Figure 3. Regarding frequency for muscle hypertrophy, there was
strong evidence that ‘fractional’ outperforms ‘total’ (2 x Log(BF) = 9.96) and very strong
evidence that ‘fractional’ outperforms ‘direct’ (2 x Log(BF) = 10.82). Regarding frequency for
muscle strength, there was very strong evidence that ‘fractional’ outperforms ‘total’ (2 x
Log(BF) = 31.27) and ‘direct’ (2 x Log(BF) = 54.84). Regarding weekly set volume for muscle
hypertrophy, there was strong evidence that ‘fractional’ outperforms ‘total’ (2 x Log(BF) =
9.48) and very strong evidence that ‘fractional’ outperforms ‘direct’ (2 x Log(BF) = 10.29).
Regarding weekly volume for muscle strength, there was very strong evidence that
‘fractional’ outperforms ‘total’ (2 x Log(BF) = 18.21) and ‘direct’ (2 x Log(BF) = 45.96). Given
the evidence was strongest for the ‘fractional’ model, the following sections will focus on
the results for this quantification method. Results for ‘total’ and ‘direct’ can be found in the
supplementary materials (https://osf.io/6z3xu).
4.5 Frequency Analysis
The following sections will present the results of meta-regression models for the effects of
‘fractional’ frequency on hypertrophy and strength. Specifically, we will indicate the best fit
of the candidate models; then, we will evaluate the overall quality of the model fit (i.e., R2)
and the marginal slope for the main effect of frequency (i.e., the slope at the mean of
frequency after adjusting for volume, intervention duration, and training status). Full model
summary tables with extracted estimates can be found in the supplementary materials
(https://osf.io/6z3xu).
Method of Quantifying Weekly Set Volume Model Comparisions
A
B
Hypertrophy (Numerator)
Strength (Numerator)
Fractional
Direct
Total
Fractional
Direct
Total
9.48
−0.8
0
18.21
−27.75
0
2 x Log(BF)
Total
10
5
Denominator
0
−5
−10
Direct
10.29
0
0.8
45.96
0
27.75
2 x Log(BF)
25
0
Fractional
0
−10.29
−9.48
0
−45.96
−18.21
−25
Kass and Raferty (1995) Scale: −Inf to 0 = Negative; 0 to 2 = Weak; 2 to 6 = Positive;
6 to 10 = Strong; 10 to +Inf = Very Strong; Positive Values Favor Numerator
Method of Quantifying Frequency Model Comparisions
A
B
Hypertrophy (Numerator)
Strength (Numerator)
Fractional
Direct
Total
Fractional
Direct
Total
9.96
−0.85
0
31.27
−23.57
0
2 x Log(BF)
Total
10
5
Denominator
0
−5
−10
Direct
10.82
0
0.85
54.84
0
23.57
2 x Log(BF)
50
25
0
Fractional
0
−10.82
−9.96
0
−54.84
−31.27
−25
−50
Kass and Raferty (1995) Scale: −Inf to 0 = Negative; 0 to 2 = Weak; 2 to 6 = Positive;
6 to 10 = Strong; 10 to +Inf = Very Strong; Positive Values Favor Numerator
Figure 3: Relative evidence for models using the Kass and Raftery scale: < 0 = negative evidence in favor of the numerator; 0 < 2 =
weak evidence in favor of the numerator; 2 < 6 = positive evidence in favor of the numerator; 6 < 10 = strong evidence in favor of
the numerator; ≥ 10 = very strong evidence in favor of the numerator.
4.5.1 Frequency: Muscle Hypertrophy Outcomes
The multilevel meta-regression models for the effect of ‘fractional’ frequency on
hypertrophy included 35 studies, 220 effects, and 1,032 participants. Model comparisons
revealed the reciprocal model was the best fit (Figure 4). The fixed effects of the model
explained less than a quarter of the total variance (R2marginal = 21.9%; R2conditional = 73.1%). The
marginal slope was positive with a 91.3% probability the linear slope is greater than 0; thus,
the credible interval contained the null point estimate (β = 0.32% [95% CrI: -0.14%, 0.82%]).
The best fit model and slope indicates that hypertrophy may exhibit a positive
dose-response relationship with increasing weekly frequency but the effect is inconsistent
and compatible with negligible effects.
The additional models containing only direct effects — two-stage meta-regression and
contrast-based meta-analysis — included 15 studies, 78 effects, and 370 participants. These
models confirm the compatibility with negligible effects found in the primary
meta-regression and can be found in the supplementary materials (https://osf.io/rakvh).
4.5.2 Frequency: Muscle Strength Outcomes
The multilevel meta-regression models for the effect of ‘fractional’ frequency on strength
included 66 studies, 490 effects, and 2,020 participants. Model comparisons revealed the
reciprocal model was the best fit (Figure 4). The fixed effects of the model explained about
a quarter of the total variance (R2marginal = 25.7%; R2conditional = 75.1%). The marginal slope was
positive with a 100% probability the linear slope is greater than 0; thus, the credible interval
did not contain the null point estimate (β = 3.27% [95% CrI: 2.74%, 3.84%]). The best fit
model and slope indicates that strength exhibits a dose-response relationship with
increasing weekly frequency with diminishing returns.
The additional models containing only direct effects — two-stage meta-regression and
contrast-based meta-analysis — included 27 studies, 148 effects, and 700 participants.
These models qualitatively confirm the primary meta-regression results and can be found
in the supplementary materials (https://osf.io/wt6y9).
Control Adjusted Marginal Effects for Fractional Frequency (Hypertrophy)
Exponentiated Response Ratio (%∆ Muscle Size)
A
B
10
0
−10
0
2
4
6
−1.5
Weekly Frequency Per Muscle Group (Fractional)
−1.0
−0.5
0.0
0.5
1.0
1.5
Mean Linear Slope (%∆ Muscle Size Per Session)
Control Adjusted Marginal Effects for Fractional Frequency (Strength)
Exponentiated Response Ratio (%∆ Maximal Strength)
A
B
50
25
0
0
2
4
Weekly Frequency Per Muscle Group (Fractional)
6
−5.0
−2.5
0.0
2.5
5.0
Mean Linear Slope (%∆ Maximal Strength Per Session)
Figure 4: Fractional weekly frequency best fit multilevel meta-regression for hypertrophy (reciprocal model) and strength
(reciprocal model) analyzed as an exponentiated response ratio. Data are presented as estimated marginal means (solid line) with
95% quantile-based compatibility intervals (light band = credible, dotted band = prediction) after adjusting for volume, intervention
duration, and training status. Colored circles represent the effect size of each observation included in the analysis, with the size of
each circle representing its weight determined by inverse variance weighting. Panels labeled B represent the linear slope at the
mean value of fractional frequency for all effects. In all panels, the main effect for fractional frequency is presented at the mean of
the continuous fixed effects (i.e., fractional volume and intervention duration) and proportionally marginalized across the
categorical fixed effect (i.e., training status).
4.6 Volume Analysis
The following sections will present the results of meta-regression models for the effects of
‘fractional’ weekly set volume on hypertrophy and strength. Specifically, we will indicate the
best fit of the candidate models; then, we will evaluate the overall quality of the model fit
(i.e., R2) and the marginal slope for the main effect of volume (i.e., the slope at the mean of
volume after adjusting for frequency, intervention duration, and training status). Full model
summary tables with all extracted estimates can be found in the supplementary materials
(https://osf.io/6z3xu).
4.6.1 Volume: Muscle Hypertrophy Outcomes
The multi-level meta-regression models for the effect of ‘fractional’ weekly set volume on
hypertrophy included 35 studies, 220 effects, and 1,032 participants. Model comparisons
revealed the square root model was the best fit (Figure 5). The fixed effects of the model
explained about a quarter of the variance (R2marginal = 22.3%; R2conditional = 73.3%). The marginal
slope was positive with a 100% probability the linear slope is greater than 0; thus, the
credible interval did not contain the null point estimate (β = 0.24% [95% CrI: 0.15%, 0.33%]).
The best fit model and slope indicates that hypertrophy exhibits a dose-response
relationship with increasing weekly volume with diminishing returns. The degree of
diminishing returns relative to the SDES is displayed in Table 2A.
The additional models containing only direct effects — two-stage meta-regression and
contrast-based meta-analysis — included 17 studies, 121 effects, and 544 participants.
These models qualitatively confirm the primary meta-regression results and can be found
in the supplementary materials (https://osf.io/47zgs).
4.6.2 Volume: Muscle Strength Outcomes
The multilevel meta-regression models for the effect of ‘fractional’ weekly set volume on
strength included 66 studies, 490 effects, and 2,020 participants. Model comparisons
revealed the reciprocal model was the best fit (Figure 5). The fixed effects of the model
explained about a quarter of the variance (R2marginal = 26.1%; R2conditional = 74.8%). The marginal
slope was positive with a 100% probability the linear slope is greater than 0; thus, the
credible interval did not contain the null point estimate (β = 0.21% [95% CrI: 0.16%, 0.26%]).
The best fit model and slope indicates that strength exhibits a dose-response relationship
with increasing weekly volume with strong diminishing returns and a functional plateau.
The degree of diminishing returns relative to the SDES is displayed in Table 2B.
The additional models containing only direct effects — two-stage meta-regression and
contrast-based meta-analysis — included 32 studies, 257 effects, and 972 participants.
These models qualitatively confirm the primary meta-regression results and can be found
in the supplementary materials (https://osf.io/sbqxy).
4.6.3 Volume: Interacting Moderators
Data visualization from all interaction moderator analyses for the effects of ‘fractional’
weekly set volume can be found in the supplementary materials (https://osf.io/6z3xu).
These analyses should be interpreted with caution, as the number of observations that
contribute to the effects are substantially reduced when compared to the main models,
thereby reducing the precision of the estimates. Further, there were often no direct
examinations of these interactions and we did not attempt to uniquely isolate the causal
effect in the case of each moderator. Therefore, we view the role of these exploratory
moderators primarily to generate future hypotheses.
Control Adjusted Marginal Effects for Fractional Weekly Set Volume (Hypertrophy)
Exponentiated Response Ratio (%∆ Muscle Size)
A
B
20
10
0
−10
0
10
20
30
40
−0.25
Weekly Set Volume Per Muscle Group (Fractional)
0.00
0.25
Mean Linear Slope (%∆ Muscle Size Per Set)
Control Adjusted Marginal Effects for Fractional Weekly Set Volume (Strength)
Exponentiated Response Ratio (%∆ Maximal Strength)
A
B
50
25
0
0
10
20
30
Weekly Set Volume Per Muscle Group (Fractional)
−0.2
0.0
0.2
Mean Linear Slope (%∆ Maximal Strength Per Set)
Figure 5: Fractional weekly set volume best fit multilevel meta-regression for hypertrophy (square root model) and strength
(reciprocal model) analyzed as an exponentiated response ratio. Data are presented as estimated marginal means (solid line) with
95% quantile-based compatibility intervals (light band = credible, dotted band = prediction) after adjusting for frequency,
intervention duration, and training status. Colored circles represent the effect size of each observation included in the analysis,
with the size of each circle representing its weight determined by inverse variance weighting. Panels labeled B represent the linear
slope at the mean value of fractional volume for all effects. In all panels, the main effect for fractional volume is presented at the
mean of the continuous fixed effects (i.e., fractional frequency and intervention duration) and proportionally marginalized across
the categorical fixed effect (i.e., training status).
Table 2A: Volume Efficiency Tiers for Hypertrophy
Tier
Minimum Effective Dose
Fractional Weekly
Sets
4
Description
Sufficient to elicit detectable hypertrophy
Higher Efficiency
5 - 10
~6 additional weekly sets required for additional detectable hypertrophy
Intermediate Efficiency
11 - 18
~8.5 additional weekly sets required for additional detectable hypertrophy
Lower Efficiency
19 - 29
~10.75 additional weekly sets required for additional detectable hypertrophy
Lowest Efficiency
30 - 42
~12.5 additional weekly sets required for additional detectable hypertrophy
Unclear
43 +
Insufficient data to inform efficiency or potentially less hypertrophy
Table 2B: Volume Efficiency Tiers for Strength
Tier
Fractional Weekly
Sets
Description
Minimum Effective Dose
1
Sufficient to elicit detectable strength gain
Higher Efficiency
2
~0.75 additional weekly set required for additional detectable strength gain
Intermediate Efficiency
3-4
~2.25 additional weekly sets required for additional detectable strength gain
Lower Efficiency
5-?
Additional weekly sets do not consistently enhance strength gains > SDES
The minimum effective dose was defined as the volume at which the estimated marginal mean exceeds the
Smallest Detectable Effect Size (SDES). The SDES is 2.05% for hypertrophy and 3.96% for strength. Volume
efficiency tiers were determined by the number of additional sets required for an incremental increase in the
estimated marginal mean that exceeds the SDES.
5 DISCUSSION
The present meta-regressions explored the dose-response relationships of RT volume
(weekly sets) and frequency (sessions per week) on the effects of muscle hypertrophy and
strength gains. As volume increases, our results indicate that both muscle hypertrophy and
strength gains tend to increase; however, the diminishing returns are stronger for strength
gains. As frequency increases, our results indicate that there is a negligible effect for
muscle hypertrophy but a meaningful effect with diminishing returns for strength gains.
These relationships can inform future research and the conceptual understanding for
practitioners in regard to how RT dosage influences muscle hypertrophy and strength
gains.
5.1 Volume/Frequency Quantification Methods
Set volume and frequency have typically been quantified as the number of sets and
sessions per muscle group/movement per week, respectively (1,3,6,7,14–18,108).
Descriptions of these quantifications have been rather general, and given accurately
exploring the RT dose-response requires accuracy of the independent variables, the
present study explored multiple volume/frequency quantification methods. Each RT set
was classified as direct or indirect based on its specificity to the hypertrophy or strength
measurement. Then, weekly volume/frequency for indirect sets was quantified as 1 for
‘total,’ 0.5 for ‘fractional,’ and 0 for ‘direct.’ As a result, ‘total’ refers to the RT dosage with
any meaningful involvement of the measured muscle for hypertrophy or the muscle(s)
involved in the strength assessment. ‘Direct’ refers specifically to the primary force
generator in the exercise for hypertrophy or the exact exercise assessed for strength.
‘Fractional’ represents a balance between ‘total’ and ‘direct.’
All Bayes Factors, used to quantify the relative support for one model over another,
favored the models for the ‘fractional’ quantification method. The support for the
‘fractional’ quantification method can be categorized as ‘strong,’ or ‘very strong’ per the
Kass and Raftery scale (52). Indeed, it is unlikely that any involvement of a muscle group in
an RT set should be quantified equally for muscle hypertrophy (10–13). For instance, direct
sets are likely to expose the primary force-generating muscle to a closer proximity to
failure, which may enhance the hypertrophic training stimulus (109). Regarding muscle
strength, indirect sets generally contribute to the strength assessment but are unlikely to
be as effective as the specific movement (10,11,110).
In addition to practical insight for volume/frequency quantification for researchers and
practitioners, the present study provides indirect evidence into the effects of direct vs.
indirect sets on muscle growth and strength gains. Specifically, it appears that on average,
the hypertrophic and strength stimulus of an indirect set is close to half the effect of an
indirect set. However, the ‘fractional’ quantification method suffers from the assumption
that all indirect training should be quantified as half a set. Therefore, future research may
wish to investigate factors influencing the stimulus from indirect sets.
5.2 Frequency & Hypertrophy Dose-Response
The primary meta-regression indicated an inconsistent dose-response relationship
between weekly ‘fractional’ frequency and muscle hypertrophy, with a reciprocal model as
the best fit and a 91.3% posterior probability the linear slope is greater than zero. While
this indicates a potential slight positive effect of frequency, it should be noted that: i) the
credible interval of the marginal slope was compatible with negligible effects, and ii) the
contrast-based meta-analysis and two-stage meta-regression of only direct effects did not
indicate an effect of frequency. In aggregate, our results suggest that any independent
effect of additional frequency is small and is not consistently identifiable across modeling
methods.
These results align with previous meta-analyses (19,111) and are most comparable to a
2019 meta-analysis by Schoenfeld et al. (14) reporting no significant effect of frequency in
volume-equated studies utilizing direct hypertrophy measures (ES = 0.07 [95% CI: -0.08,
0.21]). The present meta-analysis utilizes additional data and bolsters the lack of a
consistently identifiable independent effect of frequency on muscle hypertrophy. However,
the 91.3% likelihood the linear slope is greater than 0 for the primary meta-regression,
along with the wide uncertainty interval of the linear slope, permits additional study into
the potential programming configurations (e.g., muscle group trained, training status,
proximity to failure) that may elicit greater muscle hypertrophy with higher frequencies.
Although more data is needed to conclusively establish the dose-response of frequency on
hypertrophy, other data can be considered to generate hypotheses for future studies.
Mechanistic data indicate that muscle protein synthesis (MPS) is meaningfully reduced 48
hours after an RT bout in untrained individuals (112) and may even return to baseline in
trained individuals (113,114). When paired conceptually with the lack of a consistent,
independent effect of frequency in the present meta-analysis, multiple potential
explanations exist. These include: i) the MPS timelines reported in acute research do not
necessarily represent hypertrophic effects, perhaps in part or entirely related to muscle
damage repair confounding MPS elevations (115); ii) the collective training status of the
included participants was not sufficiently advanced, resulting in an extended anabolism
period post-training, which may have obscured the beneficial effects of higher frequency;
iii) there is no plateau in hypertrophy with increasing per session volumes; iv) the average
weekly ‘fractional’ set volume of 13.00 ± 8.87 in the included studies may have resulted in
per session volumes that were either too high or too low, preventing beneficial effects of
higher frequencies to be observed (116); v) an unidentified negative effect of higher
frequency counteracts the theoretical positive effects. Please refer to our parallel project
for additional insight on the effects of per session volume (117).
5.3 Frequency & Strength Dose-Response
The primary meta-regression indicated a positive dose-response relationship between
weekly ‘fractional’ frequency and strength gains, with a reciprocal model as the best fit and
a 100% posterior probability of the marginal slope exceeding zero. This, along with the
contrast-based meta-analysis and two-stage meta-regression finding positive effects of
frequency, indicates a dose-response relationship between frequency and strength gain.
This finding is in contradiction to previous meta-analyses on the independent effects of
frequency on strength gains (16–18) and adds additional insight to analyses reporting a
significant effect (111). Across these previous meta-analyses, no consensus exists on the
definition of frequency, and whether indirect training (i.e., exercises different from the
strength assessment but training the involved muscles) counts towards weekly frequency
has remained inconsistent.
The inclusion criteria and statistical analysis used in the present meta-regressions most
closely align with a meta-regression by Grgic et al. (17), which reported no statistically
significant relationship (p = 0.421) between frequency and 1RM strength gains in
volume-equated studies. However, instead of necessarily different findings, the present
meta-regressions build off of this analysis by exploring nonlinear models, a novel frequency
quantification method, and additional data. Indeed, the effect size reported by Grgic et al.
(17) increased notably from a frequency of 1 (ES = 0.53 [95% CI: 0.13, 0.93]) to a frequency
of 2 (ES = 0.80 [95% CI: -0.25, 1.86]), which aligns with the increase seen in the control
adjusted estimates for the reciprocal best fit model when increasing from a ‘fractional’
frequency of 1 (ES = 12.72% [95% CrI: 10.57%, 15.05%]) to 2 (ES = 17.32% [95% CrI: 14.34%,
20.56%]). Beyond this point, accelerating diminishing returns occur.
Higher frequencies allow for more frequent practice with the assessed exercise or a similar
motor pattern. Indeed, simply practicing the test provides a robust stimulus for strength
gains (118). The dose-response relationship found in the present meta-analysis indicates
that additional exposures, and not simply additional sets, can enhance strength gains albeit
with diminishing returns. Therefore, in addition to potential beneficial effects on muscular
adaptations, it is possible that higher frequencies lead to higher quality practice, ultimately
increasing training performance and therefore loads used (119). However, there is
conceivably a point in which higher frequencies do not permit sufficient recovery and
negatively impact training performance. Further research is necessary to investigate this
hypothesis.
It should be noted that the dose-response relationship between frequency and strength
gains is limited to the training protocols used in the included studies. The average weekly
‘fractional’ set volume of 8.14 ± 6.23 in the included studies is relatively low; therefore,
further analysis is required to explore the dose-response of per session volume and
strength gains. Please refer to our parallel project for additional insight on the effects of
per session volume (117).
5.4 Volume & Hypertrophy Dose-Response
The primary meta-regression indicated a positive dose-response relationship whereby
higher weekly ‘fractional’ set volumes resulted in greater muscle hypertrophy, with a 100%
posterior probability of the marginal slope exceeding zero. These findings align with
previous meta-analytic work (1,5,6,19) and expands on them by including new data and
exclusively site-specific, direct hypertrophy measures. Our analysis emphasizes
within-study, between-group effects of different volumes in our multilevel meta-regression
model structure and secondary analyses of only direct effects. These factors may explain
why the present results report a stronger dose-response relationship compared to
meta-analyses that explore the moderating effect of volume on hypertrophy in general RT
studies with inclusion criteria allowing for indirect hypertrophy measurements (108,120).
Schoenfeld et al. (1), using only muscle-specific, direct hypertrophy measurements,
analyzed weekly set volume as a continuous linear predictor, and reported a 0.38%
increase in hypertrophy per additional set. This is comparable to the marginal linear slope
in the present meta-analysis, which estimated a 0.24% increase in hypertrophy (95% CrI:
0.15%, 0.33%) per additional set at the average ‘fractional’ weekly volume of 12.25 sets. The
present meta-analysis builds upon the analysis by Schoenfeld et al. (1) by exploring
multiple functional forms, both linear and nonlinear, to inform the nature of the
dose-response. Indeed, it has been suggested that as volume increases, diminishing
marginal hypertrophy occurs, and potentially even an inverted-U in which additional
volume will attenuate hypertrophy (1,4,5,84). Mechanistic data indicates greater-post
exercise MPS and intracellular anabolic signaling for higher volume protocols in humans
(102,121–125); however, a dose-response relationship has been explored using electrically
stimulated isometric contractions in male rats, indicating a plateau in MPS but not in
p70S6K phosphorylation with additional “sets” (126). The present meta-analysis quantifies
this relationship using applied outcomes in humans and supports the notion of diminishing
returns but not an inverted-U. The best fit model, as identified by Bayesian Information
Criterion approximated Bayes Factors, was a square root model, and indicated diminishing
returns that accelerate with higher volumes. However, given the width of the credible
intervals at higher volumes, the best fit model is still compatible with multiple functional
forms (e.g., functional plateau, inverted-U).
To quantify the diminishing returns, we reported the dose-response using efficiency tiers,
which contextualize the findings based on the number of ‘fractional’ sets required for the
point estimate to exceed increments of the SDES. These tiers quantify the increasing
incremental volume needed to achieve detectable additional hypertrophy. For instance, the
volume required for the final increment of the SDES is more than three times that required
for the first increment (i.e., the minimum effective dose). Although this approach indicated
that the minimum effective dose occurs with low volume (4 ‘fractional’ weekly sets), the
tiers also indicate no clear plateau in the primary meta-regression. Instead, they suggest an
increasing number of sets needed to elicit detectable additional hypertrophy. However,
caution is warranted as few studies have explored ~25+ ‘fractional’ weekly sets. Therefore,
future research may wish to explore these higher volumes to better inform the
dose-response and potential plateau point.
Moderator analyses indicated that the marginal slope of the dose-response relationship
between weekly ‘fractional’ sets and hypertrophy was not often influenced by other
variables. However, extreme caution is warranted for all moderator analyses as by nature,
these analyses are all indirect effects. Therefore, these moderator analyses should be
viewed as hypothesis-generating; to properly explore potential moderators of the
dose-response relationship, additional studies specifically designed to do so are required.
5.5 Volume & Strength Dose-Response
The primary meta-regression indicated a positive dose-response relationship between
weekly ‘fractional’ set volume and strength gains, with a 100% posterior probability of the
marginal slope exceeding zero. However, the best fit model was reciprocal and indicated
strong diminishing returns and a functional plateau. These findings are generally consistent
with those of previous meta-analyses (7,108,127,128). Ralston et al. (7) provides valuable
insight on relatively low volumes (mean weekly direct set volume = 3.14 ± 2.63) and
reported significantly greater strength gains in groups with > 5 compared to ≤ 5 weekly sets
(ES = 0.18 [95% CI: 0.06, 0.30]). The present meta-analysis utilized a wider inclusion criteria,
higher average volumes, accounted for indirect sets via the ‘fractional’ quantification
method, and explored nonlinear dose-response relationships. As hypothesized by Ralston
et al. (7), the present meta-regression provides support for a nonlinear relationship.
Similar to muscle hypertrophy, the best fit model is still compatible with other functional
forms, including an inverted-U. Nonetheless, our findings indicate that the dose-response
relationship is strongest with low weekly set volumes. Indeed, the estimated effect of one
‘fractional’ weekly set exceeded the SDES; therefore, one set was identified as the minimum
effective dose. Additional increments in the SDES were observed up to approximately 4
‘fractional’ weekly sets, but not beyond this point. However, the SDES of 3.96% may be
greater than what some deem practically relevant; additional sets beyond this point may
produce additional strength gains, albeit less than the SDES, prior to the functional plateau.
The tabulated data provides additional insight and can be found in the supplementary
materials (https://osf.io/cf6p5).
While we did not venture to explore the mechanistic underpinnings of the dose-response
relationship, it is interesting to consider the multi-faceted nature of adaptations
contributing to muscle strength gains. Learning effects from additional direct sets, and to a
lesser extent indirect sets, are likely to contribute to strength gains (118). Furthermore,
while not unanimously agreed upon (129), greater hypertrophy from increased set volume
may contribute to strength gains (130). Conversely, higher volumes may lead to increased
fatigue, as evidenced by the beneficial effects of tapering (131). Notably, elevated fatigue
may still be present at post-testing given most of the included studies did not include a
taper.
The learning effect component may predominate in the present meta-analysis as many
participants in the included studies were presumably performing a novel strength
assessment. This may contribute to the large effect observed at one ‘fractional’ weekly set.
Indeed, in well-trained powerlifters, 1-3 direct weekly sets was insufficient to result in
meaningful strength gains, but 3-9 direct weekly sets was (132). Therefore, the minimum
effective dose and dose-response relationship in novel vs. familiar strength assessments
warrants further investigation. The moderator analysis in the present study may provide
some insight, but given they rely on indirect effects, future studies directly examining this
concept and other moderators are warranted.
5.6 Limitations & Considerations
Several limitations and considerations exist with this meta-analysis. While we have
described and quantified the dose-response relationships, it should be emphasized that
these relationships are limited to the contexts of the included studies (i.e., training
variables, participant characteristics, etc.). For instance, proximity to failure appears to be
an important variable for maximizing muscle hypertrophy (109); however, although 78.47%
of hypertrophy effects reported some form of a failure definition, only ~30% had a clear
definition of momentary failure (133). Additionally, our moderator analyses on proximity to
failure and other variables are extremely limited. Direct research is necessary to determine
whether increased hypertrophic effectiveness per set influences the functional form of the
dose-response relationships.
Additionally, we did not venture to describe potential indirect negative consequences of
high RT dosage (e.g., sustainability, injury, psychological burnout). All analyzed participants
must have tolerated the training intervention sufficiently well to receive a post-test value
and inclusion in the respective study. These considerations are exacerbated when
considering the relatively short average intervention duration of 10.42 ± 4.48 weeks.
Further, our analysis focused on site-specific training volume and not overall RT volume.
The RT protocols of many included studies were not necessarily balanced throughout the
entire body and instead biased towards contributing to improvements in the
measurement(s). It remains unclear if the site-specific dose-response relationships are
impacted by the overall RT dosage.
Individual-level practical application of these findings depends on many factors. Various
physiological factors may influence the hypertrophy or strength gains an individual
experiences from a given dosage (102), which may have downstream implications on
program requirements for maximum results. Future research may wish to explore
individual response variation to different dosages with appropriate study design (134).
Potential inherent limitations exist regarding the independent variables of the present
meta-analysis. While a primary aim was to explore the most probable model fits based on
different quantification methods of the independent variables (‘total’/’direct’/’fractional’),
limitations still exist. For instance, volume and frequency were quantified on a weekly time
scale, but any choice of time period for quantifying volume and frequency is arbitrary.
Therefore, a parallel project by our group explores the dose-response relationships of set
volume per session on muscle hypertrophy and strength gains (117).
Limitations also exist with the dependent variables used in the present meta-analysis. For
instance, while only direct measures of muscle size were used, which are likely more
sensitive to hypertrophy (1,135), other factors may influence muscle size measurements
(136). For instance, edema sufficient to confound muscle size measurements in the days
following training has been reported in novel, highly damaging eccentric training protocols
(137–139). While edema is unlikely to be a major confounder in trained individuals
following an 8-set training session (140,141) or in previously untrained participants by the
end of a typical training study (142), cautious interpretation of the present results is
warranted. This is especially notable given the paucity of data exploring edema’s effect on
muscle size measurements following higher volume RT.
Although best fit models have been identified, it should be noted that each dose-response
relationship remains compatible with multiple functional forms, especially upon the
addition of new data at volume/frequency levels with limited data. In particular, additional
hypertrophy studies including untrained, non-training control groups are warranted to
better inform the initial dose-response.
6 CONCLUSIONS
The dose-response relationships describing the effects of weekly volume and frequency on
muscle hypertrophy and strength gains are best represented with the ‘fractional’
quantification method, where indirect sets are counted as half a set. For muscle
hypertrophy, there is a positive dose-response relationship between ‘fractional’ set volume
and muscle hypertrophy, though with diminishing returns. No clear plateau in the
dose-response relationship was identified; however, there is additional uncertainty at
higher volumes. Increasing ‘fractional’ frequency, on a volume adjusted basis, appears to
have a negligible effect on muscle hypertrophy. For muscle strength, there is a positive
dose-response relationship between ‘fractional’ set volume and strength gains, but with
strong diminishing returns and a functional plateau. ‘Fractional’ frequency also has a
positive dose-response for strength gains, though with diminishing returns. The modest
quality of overall model fits and the width of the uncertainty intervals suggest that multiple
dose-response forms are compatible with the present analysis, particularly upon the
addition of future data.
Data and Supplementary Material Accessibility
All materials, data, and code are available on the Open Science Framework project page
(https://osf.io/6z3xu).
Author Contributions
JP conceptualized the project, extracted data, assisted with the statistical analysis, and
wrote the manuscript. JR conceptualized the project, extracted data, and reviewed the
manuscript. ZR conceptualized the project, performed the statistical analysis, and reviewed
the manuscript. SH extracted data and reviewed the manuscript. MZ reviewed the
manuscript.
Conflict of Interest
Joshua Pelland, Jacob Remmert, Zac Robinson, Seth Hinson, and Michael Zourdos are
coaches and writers in the fitness industry.
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